Ordering Cards
1 out of 3
This problem is designed to help children to learn, and to use, the two and three times tables.
Problem
Ordering Cards printable loop cards
Look at these cards.
7 ×2 | 3 ×6 | 12 ÷3 | 14 −2 |
4 ×2 | 20 +1 | 10 ×2 | 5 ×2 |
8 −5 | 15 ÷3 | 21 ÷3 | 18 −3 |
Can you sort them so that they follow round in a loop?
Here is a card from a different set.
10 ×3 |
What number would follow it?
What about this one? What would follow it?
12 ÷2 |
What calculation might be on the card before this one?
Getting Started
Student Solutions
This challenge obviously led to some interesting explorations! Here's a solution sent in by Maicy, Caitlan and Taryn from Saxmundham Primary School in England
| Calculation | Method | Answer |
| 3 x 6 | mental | 18 |
| 18 - 3 | mental | 15 |
| 15 ÷ 3 | mental | 5 |
| 5 x 2 | mental | 10 |
| 10 x 2 | mental | 20 |
| 20 + 1 | mental | 21 |
| 21 ÷ 3 | mental | 7 |
| 7 x 2 | mental | 14 |
| 14 - 2 | mental | 12 |
| 12 ÷ 3 | mental | 4 |
| 4 x 2 | mental | 8 |
| 8 - 5 | mental | 3 |
if you use this card from another set $10 \times 3$ the card that follows is $30$.
if you use this card from another set $12 \div 2$ the card what follows is $6$
Myles, Joshua and William, also from Saxmundham Primary School from England, sent in:
| Sum | Method | Answer |
| 7 x 2 | mental | 14 |
| 14 - 2 | mental | 12 |
| 12 \div 3 | mental | 4 |
| 4 x 2 | mental | 8 |
| 8 - 5 | mental | 3 |
| 3 x 6 | mental | 18 |
| 18 - 3 | mental | 15 |
| 15 \div 3 | mental | 5 |
| 5 x 2 | mental | 10 |
| 10 x 2 | mental | 20 |
| 20 + 1 | mental | 21 |
| 21 \div 3 | mental | 7 |
If we used the card from a different set $10 \times 3$ it would make $30$.
If we used $12 \div 2$ it would make $6$.
Ashton from Raynsford Voluntary Controlled First School in England sent in this solution:
I started with $8 - 5$ at that $3$ then I found the problem starts with $3$
and that was $3 \times 6$ then I work it out and then I did what you have just done
again so it will be $18 - 3$ then $15 \div 3$ then $5 \times 2$ then $10 \times 2$ then $20 + 1$ then $21 \div 3$
then $7 \times 2$ then $14 - 2$ then $12 \div 3$ then $4 \times 2$ then $8 - 5$ and that is what we started
with at the beginning so we have finish the loop game.
Thank you for these well thought out solutions. Thank you also to those who pointed out that we had slipped up on day $1$ with an incorrect card.
Teachers' Resources
Using NRICH Tasks Richly describes ways in which teachers and learners can work with NRICH tasks in the classroom.
Why do this problem?
This problem is designed to help children to learn, and to use, the two and three times tables.
Possible approach
You could print out the sheet of cards and cut it into the twelve separate cards and give the individual cards to the group to work on in pairs, so that they are able to talk through their ideas with a partner.
The cards should form a loop so it does not matter which card is used to start. If you want to make the loop longer, or make your own loop, you could download these similar blank cards.
If you lengthen the loop you will need to take out one card and replace it with your new ones. Try to avoid repeating a number which has been used already, and avoid multiplying and then immediately dividing by the same number.
Key questions
Which card did you start with?
How does your sequence of numbers go?
Look carefully at the loop here and check your answers.
Possible extension
Learners could make their own set of looping cards using the blank cards.
Possible support
Some children might benefit from having a written version of the two and three times tables to help them, or using a calculator.